A design method of a primary-mirror position control system based on motor-driven hydraulic support is proposed to meet the high precision requirements of the primary mirror position in mirror imaging of a 4 m large telescope. Firstly, the composition of the primary-mirror position control system is introduced, and the mathematical model of each structure is established. Furthermore, a primary-mirror position controller is designed based on the first-order dynamic sliding mode control and a linearly extended observer. Finally, the system is simulated. The results show that the maximum tracking error of each support area is less than 0.5 μm when the tilt axis moves at a uniform speed of 1 (°)·s ^-1. Besides, in the case of sinusoidal guidance of the tilt axis, the maximum tracking error is 1 μm, which is better than the tracking error (13 μm) of the traditional proportional-integral control. The results satisfy the design requirements of the proposed system in the 4 m large telescope, providing a reference for the design of a primary-mirror position control system in a large telescope.